Which graph represents the function of f(x) = the quantity of 4 x squared minus 16, all over 2 x minus 4 ? (2 points) graph of 2 x plus 4, with discontinuity at negative 2, 0 graph of 2 x plus 4, with discontinuity at 2, 8 graph of 2 x minus 4, with discontinuity at negative 2, negative 8 graph of 2 x minus 4, with discontinuity at 2, 0
Answers
We can simplify the given rational function into a linear one, the graph is below.
Which graph represents the function?
Here we have the rational function:
[tex]f(x) = \frac{4x^2 - 16}{2x - 4}[/tex]
Factorization the numerator, we get:
4x² - 16 = 0
4x² = 16
x² = 16/4 = 4
x = ±√4 = ±2
Then the numerator can be written as:
4*(x - 2)*(x + 2)
And the denominator can be rewritten as:
2x - 4 = 2*(x - 2)
Then the function becomes:
[tex]f(x) = \frac{4*(x + 2)*(x - 2)}{2*(x - 2)} \\\\f(x) = 2*(x + 2) = 2x + 4[/tex]
So we have just a linear equation, so the graph that represents the function is the graph of a line, the one you can see below.
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Related Questions
what term is defined by the formula b^2 = a^2 + c^2 - 2ac(cosB)
Answers
Answer:
It is cosine theorem
Step-by-step explanation:
It is cosine theorem.
Last year, about 2,400 people participated in a local event. This year, about 3,200 people participated. What was the approximate percent increase in participation?
Answers
Answer:
33 %
Step-by-step explanation:
3200 - 2400 = 800
800 / 2400 x 100
1 /3 x 100
100/ 3
33 %
1. Given
G(n) = 4n-5
H(n) = 2n + 1
Find G(H(8))
Answers
Answer:
first H(8)= 2×8+1=16+1=17
and G(17)= 4×17-5=68-5=63
On a coordinate plane, a line goes through points (negative 2, negative 2) and (4, 2).The graphed line can be expressed by which equation?
Answers
Answer:
y=⅔m-8 or 3y=2m-8
Step-by-step explanation:
put both equations in the form y=mx+c and solve simultaneously. when done, you will recive values for m and c. replace those values into y=mx+c
What is the slope of (6,0) and (1,3)
Answers
Answer:
- 3/5
Step-by-step explanation:
(y2-y1) / (x2-x1)
(6,0) & (1,3)
(3-0) / (1-6)
3/-5
- 3/5
The terminal side of angle θ intersects the unit circle in the first quadrant at (16/19,y). What are the exact values of sinθ and cosθ?
Answers
The exact value of sin θ and cos θ is: sinθ =(√105)/19 and cosθ =16/19
The terminal side of an angle is the angle at the standard position. The terminal side of an angle θ drawn in angle standard position is the side which isn't the initial side.
Given that the point of intersection of the terminal side of θ an the unit circle is:
(16/19,y)
The exact value of sin θ and cos θ is: sinθ =(√105)/19 and cosθ =16/19
The given parameters is represented by:
(16/19,y)
This means that :
(cosθ ,sinθ )=(16/19,y)
Using the following trigonometric identity:
cos²θ +sinθ =1
We have:
(16/19)²+y²=1
Expand fraction:
(256/361)+y²=1
Collect like terms:
y²=1-(256/361)
Take LCM:
y²=(361-256)/361
y²=105/361
Take square roots
y=(√105)/19
Substitute value for y in
(cosθ ,sinθ )=(16/19,y)
By comparison:
cosθ =16/19
sinθ =(√105)/19
So the exact value of sin θ and cos θ is: sinθ =(√105)/19 and cosθ =16/19
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what is the surface area of the walls of a hall measuring length 14m,width9m and height 4m?
Answers
Answer:
184 m²
Step-by-step explanation:
lateral area of a prism = perimeter of base × height
A = 2(14 m + 9m) × 4 m
A = 184 m²
Question Write an equation of the line that passes through (1, −2) and is parallel to the line y=7x+7. An equation of the parallel line is y= .
Answers
Answer:
Step-by-step explanation:
7 = (y+2)/(x-1)
Parallel lines have equal slopes.
You can "massage" the form into any form you need.
How would you limit the domain to
make this function one to one?
f(x) = 5-x²
Your answer will be the point to which you would
limit the function. So if you would restrict the
domain to either all x values greater than or equal
to two or all x values less than or equal to two, you
would simply enter 2.
Answers
Answer:
0
Step-by-step explanation:
You need to restrict the domain to one side of the axis of symmetry.
Please help!!! Select the quadratic equation that has no real solution.
Answers
Answer:
2x² + 6x + 20
Step-by-step explanation:
See the picture
20) Sue had these expenditures for her car: April, $138.49; May, $356.75; June, $272.35; July, $417.28. What was
her average monthly expense for her car?
a.) $276.22
b.) $296.22
c.)$286.22
Answers
given the function f(c)=4|x-5|+3, for what values of x is f(x)=15?
Answers
15=4|x-5|+3 then solve for x
12=4|x-5|
3=|x-5|
3=x-5
-3=x-5
x=8, -2
Hope this helped :)
Ten members of Balin’s soccer team ran warm ups for practice. Each member ran the same distance. Their combined distance was StartFraction 5 Over 6 EndFraction of a mile. To find the distance that each member ran, Balin wrote the expression below.
StartFraction 5 Over 6 EndFraction divided by 10
Which expression is equivalent to Balin’s expression?
Answers
The expression that is equivalent to Balin's expression is 5/6 x 1/10.
What is the equivalent expression?Division is the mathematical operation that is used to determine the quotient of a number.
In order to determine the distance ran by each member, divide the total distance ran by the total number of people.
5/6 ÷ 10
5/6 x 1/10
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The expression is equivalent to Balin’s expression is StartFraction 5 Over 6 EndFraction divided by 10
Division of fractionCombined distance = 5/6 mileNumber of Balin’s soccer team = 10Distance each member ran = Combined distance ÷ Number of Balin’s soccer team
= 5/6 ÷ 10
= 5/6 × 1/10
= 5/60
= 1/12 mile
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Choose the most convenient method to graph the line y=−3.
Select the correct answer below:
Recognize the equation as that of a vertical line passing through the x-axis at −3
Recognize the equation as that of a horizontal line passing through the y-axis at −3
Identify the slope and y-intercept and then graph
Find the x- and y-intercepts and then graph
Answers
Answer:
Recognize the equation as that of a horizontal line passing through the y-axis at −3
Help me please im trying to do this but dont understand it at all.
Answers
The attached graph represents the graph of the function g(x)
How to determine the function g(x)?The function f(x) is an absolute value function.
An absolute value function is represented as:
y = a|x - h| + k
Where
Vertex = (h, k)
From the graph, we have:
(h, k) = (-3, -2)
So, we have:
y = a|x + 3| - 2
Also, we have:
(x, y) = (-1, 0)
So, we have:
0 = a|-1 + 3| - 2
This gives
0 = 2a - 2
Solve for a
a = 1
Substitute a = 1 in y = a|x + 3| - 2
y = |x + 3| - 2
This means that
f(x) = |x + 3| - 2
We have:
g(x) = 2f(x)
This means that:
g(x) = 2(|x + 3| - 2)
So, we have:
g(x) = 2|x + 3| - 4
See attachment for the graph of g(x)
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Identify the probability to the nearest hundredth that a point chosen randomly inside the rectangle is either in the circle or in the trapezoid.
Answers
The probability that a point is chosen randomly inside the rectangle is either in the circle or in the trapezoid is 0.23 option first is correct.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
The area of the rectangle = 30×21 = 630 square m
The total outcomes = 630 square m
The favorable outcomes = area of the circle + area of the trapezoid
= π(5)² + [(11+15)/2]×5
= 78.53 + 65
= 143.53 square m
Probability(a point chosen randomly inside the rectangle is either in the circle or in the trapezoid):
= 143.53/630
= 0.227 ≈ 0.23
Thus, the probability that a point is chosen randomly inside the rectangle is either in the circle or in the trapezoid is 0.23 option first is correct.
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Answer:
0.13
Step-by-step explanation:
I guessed and got it correct. Sorry, I cant show work, I hope it helped!! <3
Which relation is also a function
{(2,0),(3,2),(2,3)}
Answers
3,2
because each input only has one output and 2 has 0 and 3 so it is not a function that leaves 3,2.
What are the domain and range of the function f of x is equal to the quantity x squared plus 5x plus 6 end quantity divided by the quantity x plus 2 end quantity?
A- D: {x ∊ ℝ | x ≠ 2}; R: {y ∊ ℝ | y ≠ −1}
B- D: {x ∊ ℝ | x ≠ − 3}; R: {y ∊ ℝ | y ≠ 0}
C- D: {x ∊ ℝ | x ≠ −2}; R: {y ∊ ℝ | y ≠ 1}
D- D: {x ∊ ℝ | x ≠ −2}; R: {y ∊ ℝ | y ≠ 0}
Answers
The domain and range of the function f of x are equal to : (C) D: {x ∊ ℝ | x ≠ −2}; R: {y ∊ ℝ | y ≠ 1}
Meaning domainA Domain can be defined as the values or numbers that are accepted or allowed in a particular function.
A domain is very important when dealing with a function.
In conclusion, The domain and range of the function f of x are equal to (C) D: {x ∊ ℝ | x ≠ −2}; R: {y ∊ ℝ | y ≠ 1}
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Chana and Josiah started skating at the same time in the same direction, but Josiah had a head start 10 meters past the starting line. Chana skated 3 meters per second and Josiah skated 2 meters per second. What does point I represent in this context?
CORRECT (SELECTED)
Chana's distance from the starting line at a time when she is behind Josiah.
Explanation: Point I is on line b, so it does represent Chana's distance at a certain time. Also, point I is below line a, so it represents a distance that is less than Josiah's distance.
Answers
The best representation for the point I is that Chana's distance from the starting line at a time when she is behind Josiah.
How to solve for the line BThe point I is the distance of Chana at a particular point in time. This distance is the line a.
At point a, the speed is more so below it, it shows a speed that is less than the distance which Josiah has covered.
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A television game show has 12 doors, of which the contestant must pick 3. Behind 3 of the doors are expensive cars, and behind the other 9 doors are consolation prizes. The contestant gets to keep the items behind the 3 doors she selects. Determine the probability that the contestant wins at least one car.
Answers
The probability that the contestant wins at least one car is 3/5.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
For 1 car, we consider two possible outcomes:
P(1 car) = 2/6 x 4/5 + 4/6 x 2/5
P(1 car) = 8/15
For no car in either door
P(no car) = 4/6 x 3/5
P(no car) = 2/5
The probability that the contestant wins at least one car is the sum of the probability of one car and the probability of two cars:
P(2 cars) = 2/6 x 1/5
= 1/15
P(1 car) + P(2 cars) = 8/15 + 1/15
= 3/5
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For the pair of
functions, f and g, determine the domain of f + g.
f(x) = 4x + 19, g(x) = 12x + 14
Answers
Answer: (-∞,∞)
Step-by-step explanation:
f(x)=4x+19
g(x)=12x+14
f + g= 4x +19 + 12x + 14 = 16x + 33
Domain of 16x + 33 = (-∞,∞)
Use the function below to find F(3).
Answers
Hello,
Answer: D
Step-by-step explanation:
F(x) = (1/5)ˣ
F(3) = (1/5)³ = 1³/5³ = 1/125
⇒ Answer D
175g plus 0.4kg equal in grams
Answers
Answer:
575g
Step-by-step explanation:
Since we need the ans in grams first ensure that both values are in the same unit.
So convert 0.4 kg into grams by multiplying it with 1000grams.
This gives us 400g
175+400=575g
Which inequality does the shaded region correspond to?
Answers
Answer:
y < x + 1
Step-by-step explanation:
identify 2 points along the line (-1,0) and (0,1)
gradient = [tex]\frac{0-1}{-1-0} =1\\\\the \ y \ intercept = 1\\\\y=x+1\\\\[/tex]
let us choose point (0,0) which is within our origin and substitute
0 = 0 +1
0 = 1
but we know 0 < 1
so the region is well represented by : y < x + 1
Answer:
y > x + 1
Step-by-step explanation:
→ As the line is upward sloping we can eliminate the 2 negative equations options
y < x + 1 or y > x + 1
→ As the region shaded is above the line y = x + 1, it must be y > x + 1
Which table represents a linear function?
X
1
2
34
y
3 1/1/2
O
777772
X
1
2
3
4
O
11121314
X1234
y
X1234
7
6
13
21
y
0
6
16
30
Answers
Answer:
2
Step-by-step explanation:
The first table represents the linear function.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The first table represents a linear function because the slope remains constant through out the function
Hence, the first table represents the linear function.
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Convert 3 tons, 569 pounds into pounds
Answers
Answer:
6,569 pounds
Step-by-step explanation:
Ton= 2,000 pounds each
Therefore, 3 x 2,000 (pounds) = 6,000(pounds). You can use a shortcut by multiplying 3 x 2 and adding the three zeros at the end. 6,000 pounds + 569 pounds will result in 6, 569 pounds.
Maria is going to purchase celery and onions for a new black bean soup recipe. The recipe calls for 1.5 times as many pounds of onions as celery. If she has $8.10, what is the most pounds of celery she can buy if celery costs $1.80 per pound and onions cost $1.50 per pound?
Answers
The maximum pounds of celery she can buy is 3.25 pounds.
What are the linear equations that represent the question?1.5c = o equation 1
1.50o + 1.80c = 8.10 equation 2
Where:
o = pounds of onions
c = pounds of celery
How many pounds of celery can she buy?
Substitute for o in equation 2 using equation 1
1.50(1.50) + 1.80c = 8.10
2.25 + 1.80c = 8.10
1.80 = 8.10 - 2.25
1.80c = 5.85
c = 5.85 / 1.80
c = 3.25 pounds
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Which of the following rational expressions has the domain restrictions x = -6 amd x = 1?
Answers
Answer:
The answer is A)
Step-by-step explanation:
There is a domain restriction meaning the denominator should not equal to zero. If you substitute 6 and -1 into x for A) :
(1-1)(-6+6)=0
The Denominator can't be zero
Hope it helps!
Find the volume of a rank 5cm long, breadth 5cm and height 5cm
Answers
Answer:
125cm³
Step-by-step explanation:
To find volume, we multiply length × width × height
(length × breadth × height)
here, we know our length to be 5cm, our width to be 5cm, and our height to be 5cm
length : 5cm
width/breadth: 5cm
height: 5cm
so, we can multiply our values together (we can plug in our known values to the volume formula of length × width × height)
length × width × height
5 × 5 × 5= 125
*note: we write volume as cubed (unit³)
So, we know our volume is 125cm³
hope this helps! have a lovely day :)
I need help with number 10,11 and 12 !
Answers
Answer:
10- I can't really help you with that one you have to just draw it on your own.
11- a triangle can only have 1 obtuse angle because the other 2 need to be acute to connect 3 sides.
12- x=20 degrees,y=64 degrees,z=116 degrees
Step-by-step explanation:
11- 1 obtuse angle because the other 2 need to be acute to connect 3 sides.
12- x=20 degrees because of the other 20 degree angle opposite to it. y=64 degrees because 180-(20+96)=64 (all angles in a triangle add to 180). z=116 degrees because supplementary angles add to 180 degrees and Y and Z are supplementary.